7.1 Integration By Parts/53

$y=xe^{-0.4x}~~~x=0,x=1$

${\begin{aligned}\underbrace {\int _{0}^{5}xe^{-0.4x}dx} _{\begin{aligned}u&=x&dv&=e^{-0.4x}dx\\[0.6ex]du&=dx&v&={\frac {5}{2}}e^{-0.4x}\end{aligned}}\\[2ex]\end{aligned}}$

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \left [ \frac{5}{2}e^{-0.4x} \right ]+\int_{5}^{0}\frac{5}{2}e^{-0.4x}dx }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \begin{align} u &= -0.4x \\[2ex] du &= dx \\[2ex] \end{align} }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \left (-\frac{25}{2}e^{-2}-0 \right )+\frac{5}{4}\int_{5}^{0}e^{u} }